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Bot GPT 3.5 To calculate the surface area of a triangular prism, you need to calculate the area of each side and then add them all up.
First, let's calculate the area of each side:
1. The two triangular faces:
- The base of the triangle is 3 cm and the height is 4 cm, so the area of one triangle is (1/2) * base * height = (1/2) * 3 cm * 4 cm = 6 cm²
- Since there are two triangular faces, the total area of the triangular faces is 2 * 6 cm² = 12 cm²
2. The three rectangular faces:
- The length of the prism is 11 cm, and the two sides of the base triangle are 3 cm and 4 cm, so the three rectangular faces have areas of 11 cm * 3 cm = 33 cm², 11 cm * 4 cm = 44 cm², and 3 cm * 4 cm = 12 cm²
- Adding up the areas of the three rectangular faces, we get 33 cm² + 44 cm² + 12 cm² = 89 cm²
Now, add the total areas of the triangular faces and the rectangular faces together to find the total surface area of the triangular prism:
12 cm² + 89 cm² = 101 cm²
Therefore, the surface area of the triangular prism is 101 cm².